Percentages - 1 - UPSC Free MCQ Practice Test with solutions

On first ₹1,00,000 → Commission = ₹6,000
On balance (S – 1,00,000) → Commission = 0.05 × (S – 1,00,000)

So,
Total Commission = 6,000 + 0.05(S – 1,00,000)

Remittance = Sales – Commission

265000 = S – [6000 + 0.05(S – 1,00,000)]

Now, we will simplify

265000 = S – 6000 – 0.05S + 5000
265000 = 0.95S – 1000
0.95S = 266000
S = 266000 ÷ 0.95 = ₹2,80,000

Assume total number of people = 100

Percentage of young people = 28%
Number of young people = 28

Percentage of old people = 100 − 28 = 72%
Number of old people = 72

Total literates = 65% of 100 = 65

Given 25% of literates are young.

Young literates = 25% of 65
= (25/100) × 65
= 16.25

Old literates = 65 − 16.25
= 48.75

Total illiterates = 100 − 65
= 35

Old illiterates = Total old − Old literates
= 72 − 48.75
= 23.25

Required percentage = (Old illiterates / Total illiterates) × 100
= (23.25 / 35) × 100
= 66.43% ≈ 66%

Step 1: Calculate selling prices per toy

• Selling price for 8 toys after 20% discount = 80% of P = 0.80 × P

• For remaining 4 toys, after 20% discount, price = 0.80 × P

• Then additional 25% discount on this price means price = 75% of 0.80 × P = 0.75 × 0.80 × P = 0.60 × P

Step 2: Calculate total revenue from selling all 12 toys

• Revenue from first 8 toys = 8 × 0.80 × P = 6.4 × P

• Revenue from last 4 toys = 4 × 0.60 × P = 2.4 × P

• Total revenue = 6.4 × P + 2.4 × P = 8.8 × P

Given total revenue = Rs 2112, so:

8.8 × P = 2112
P = 2112 ÷ 8.8 = 240

So, labeled price per toy = Rs 240

Step 3: Calculate cost price

• Since he makes 10% profit after discounts, selling price = 110% of cost price

• Total selling price = Rs 2112

• So, 2112 = 1.10 × cost price

• Cost price = 2112 ÷ 1.10 = Rs 1920

Step 4: Calculate profit percentage if sold with no discount

• Total revenue without discount = 12 × 240 = Rs 2880

• Profit = Revenue - Cost price = 2880 - 1920 = Rs 960

• Profit percentage = (960 ÷ 1920) × 100 = 50%

No. of Characters in one line = 65

No. of characters in one sheet = No. of lines × No. of characters per line = 55 × 65

Total number of characters = No. of sheets × No. of characters in one sheet = 20 × 55 × 65 = 71500

If the report is retyped –

New sheets have 65 lines, with 70 characters per line

No. of characters in one sheet = 65 × 70

Number of pages required,

Hence, 16 pages will be required if report is retyped.

Hence, reduction of (20 – 16) = 4 pages

% reduction is = (4/20) x 100 = 20%

Monthly income = Rs. 3000

Savings in each of the first 3 months = 10% of 3000
= (10/100) × 3000
= Rs. 300

Total savings in first 3 months
= 3 × 300
= Rs. 900

Total savings required = Rs. 11400

Remaining savings after first 3 months
= 11400 − 900
= Rs. 10500

From the 4th month onward, savings increase by Rs. 50 every month.

Savings form an Arithmetic Progression (AP):

4th month saving = 300 + 50 = Rs. 350
Common difference (d) = 50

Let number of months after first 3 months be n.

Sum of AP = 10500

Using formula:
Sum = n/2 [2a + (n − 1)d]

10500 = n/2 [2(350) + (n − 1)50]

10500 = n/2 [700 + 50n − 50]

10500 = n/2 (650 + 50n)

21000 = n(650 + 50n)

21000 = 650n + 50n²

50n² + 650n − 21000 = 0

Divide by 50:

n² + 13n − 420 = 0

(n + 28)(n − 15) = 0

n = 15 (reject negative value)

Total months = 3 + 15
= 18 months

75% of a number is added to 375, then the result is the number itself.

Formula Used:

Let the number be x.

According to the question:
0.75x + 375 = x

Calculations:

0.75x + 375 = x
x - 0.75x = 375
0.25x = 375
x = 375 / 0.25
x = 1500

The number is 1500.

Trader A

• CP = 1000

• Markup = x% → SP = 1000(1 + x/100)

• Profit = 1000(x/100) = 10x

Trader B

• CP = 2000

• Markup = 2x% → MP = 2000(1 + 2x/100)

• Discount = x% → SP = MP(1 – x/100)

• Profit = 2000[(1 + 2x/100)(1 – x/100) – 1]
  = 20x – 0.4x²

Equating profits

10x = 20x – 0.4x²
0.4x² – 10x = 0
x(0.4x – 10) = 0 → x = 25 (non-zero)

 Quick verification:

• A: Profit = 1000 × 25% = 250

• B: MP = 2000 × 1.50 = 3000 → Discount 25% → SP = 2250 → Profit = 250

Hence, the answer is 25%.

Commission slabs:
First ₹2,00,000 → 8% = 16,000
Next ₹3,00,000 → 5% = 15,000

Total till ₹5,00,000 = 31,000

Let total sales = S (>5,00,000).
Extra commission = 3% of (S − 5,00,000)

Total commission = 31,000 + 0.03(S − 5,00,000)

Remitted amount:
S − commission = 7,04,000

S − [31,000 + 0.03(S − 5,00,000)] = 7,04,000
S − 31,000 − 0.03S + 15,000 = 7,04,000
0.97S − 16,000 = 7,04,000
0.97S = 7,20,000
S = 7,42,268 ≈ 7,42,000 (approx.)

Hence, option(C) is correct.

Let the number of boys = x

Then number of girls = 40% more than boys
= x + 0.4x
= 1.4x

Total students = x + 1.4x
= 2.4x

Overall pass percentage = 72%

So, total number of students who passed
= 72% of 2.4x
= 0.72 × 2.4x
= 1.728x

Now,

30% of girls failed
So, 70% of girls passed

Girls passed = 70% of 1.4x
= 0.7 × 1.4x
= 0.98x

Let the percentage of boys who passed be p%.

Boys passed = p% of x
= (p/100)x

Total passed = Boys passed + Girls passed

(p/100)x + 0.98x = 1.728x

(p/100)x = 1.728x − 0.98x

(p/100)x = 0.748x

p/100 = 0.748

p = 74.8% ≈ 75%

Let total population = 100

Employed = 60%
Unemployed = 40%

Among employed, 40% are graduates
Graduates among employed = 40% of 60
= (40/100) × 60
= 24

Among unemployed, 30% are graduates
Graduates among unemployed = 30% of 40
= (30/100) × 40
= 12

Total graduates (from given employment data)
= 24 + 12
= 36

But the question states that 48% of the total population are graduates.
Hence, we scale the graduate numbers proportionally.

Ratio of unemployed graduates to total graduates (from employment data)
= 12 / 36
= 1 / 3

Therefore, percentage of graduates who are unemployed
= (1/3) × 100
= 33.33%